Iterative Methods for the Solution of a Steady State Biofilter Model

Abstract

Biofilter modeling helps in understanding the biofiltration process and designing of full-scale biofilters. The biofilter models with complex kinetics do not have analytical solutions and numerical algorithms are typically employed to obtain approximate solutions. Therefore, the primary objective of this work is to utilize two iterative schemes known as the Adomian decomposition method and the Green’s function fixed point iteration method. The proposed iterative schemes were used to find approximate solutions for a biofilter model proposed by Mohseni and Allen with methanol and alpha-pinene being the objective pollutants. The proposed schemes were applied to reproduce the concentration profiles of methanol and alpha-pinene along the biofilter column. The numerical results were compared against experimental data obtained from literature and the original model solutions. For the biofiltration of methanol, both methods were able to provide accurate predictions. As for the biofiltration of alpha-pinene, the Adomian decomposition method was not able to describe the biodegradation of alpha-pinene in the biofilter where the solution deteriorated as we moved away from the entrance region. Unlike the Adomian decomposition method, the Green’s function fixed point iteration method showed excellent prediction of alpha-pinene removal along the biofilter height. Moreover, the performance of the biofilter was tested at various conditions by determining the impact of several parameters on the biofiltration process. The simulation showed that a maximum methanol elimination capacity of 285.15 g.m-3 h-1 was achieved at an inlet loading of 300 g.m-3 h-1. Based on the sensitivity analysis study, it was observed that a complete removal of methanol in the biofilter was accomplished at 50 seconds empty bed residence time, 63 m2.m-3 biofilm surface area, 6.00 10-6 m2.h-1 diffusion coefficient and 0.01 air-biofilm partition coefficient, respectively. In conclusion, the comparison of the results demonstrated higher potential for application of the Green’s function fixed point iteration method over the Adomian decomposition method in solving biofilter models and understanding of the biofiltration process.